How to combine or replace "Diffuse" BSDF with "Emission" on model that uses normal maps?
You could use vector maths to affect the strength of the Emission based on how close the Incoming ray is to the Normal using a setup similar to the following :



Note that I've used a Bump node to generate the normal - rather than a normal map - but the same principle applies.

The Incoming ray is the ray (in world space) projecting from the camera to the surface. The Dot Product compares the Incoming ray with the Normal and produces an output that varies based on how closely those vectors are to being in the same direction. The Power node is set to 'Clamp' to prevent negative values (where the ray is effectively from the 'back' of the surface) and changing the Value allows the strength of the effect to be adjusted.



In order to change the direction of the apparent illumination and shadows you can add a Mapping node and set the rotation as desired :